Question: What is the value of the digit $K$ that will make the number $481,5K6$ divisible by $2, 3, 4$ and $9$?
Explanation: A number is... divisible by 2 if its last digit is divisible by 2, which is satisfied here. divisible by 4 if its last two digits are divisible by 4, so we must have $10K+6$ be a multiple of 4. divisible by 3 if the sum of its digits is a multiple of 3, so we must have $4+8+1+5+K+6=24+K$ be a multiple of 3, so $K$ must also be a multiple of 3. divisible by 9 if the sum of its digits is a multiple of 9, so we must have $24+K$ be a multiple of 9, so $K$ must be 3 more than a multiple of 9. Letting $K=3$ satisfies all of the above requirements, so $K=\boxed{3}$.